The 5
is divided into the 8x4,
so split the numerator and denominator by using subtraction:

Don't take the exponent
out front yet; it is only on the x,
not the 8,
and you can only take the exponent out front if it is "on"
everything inside the log. The 8
is multiplied onto the x4,
so split the factors by using addition:

log2(8x4)
– log2(5) = log2(8)
+ log2(x4)
– log2(5)

The x
has an exponent (which is now "on" everything inside its log),
so move the exponent out front as a multiplier:

log2(8)
+ log2(x4)
– log2(5)

= log2(8) + 4log2(x)
– log2(5)

Since 8
is a power of 2,
I can simplify the first log to an exact value:

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log2(8)
+ 4log2(x) – log2(5)

= 3
+ 4log2(x) – log2(5)

Each log contains only
one thing, so this is fully simplified. The answer is:

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